Published December 8, 2014
Genetic parameters for calving rate and calf survival from linear, threshold, and logistic models in a multibreed beef cattle population1 J. L. L. Guerra,*2 D. E. Franke,*3 and D. C. Blouin† *Departments of Animal Sciences, and †Experimental Statistics, Louisiana State University Agricultural Center, Baton Rouge 70803
ABSTRACT: Generalized mixed linear, threshold, and logistic sire models and Markov chain, Monte Carlo simulation procedures were used to estimate genetic parameters for calving rate and calf survival in a multibreed beef cattle population. Data were obtained from a 5-generation rotational crossbreeding study involving Angus, Brahman, Charolais, and Hereford (1969 to 1995). Gelbvieh and Simmental bulls sired terminal-cross calves from a sample of generation 5 cows. A total of 1,458 cows sired by 158 bulls had a mean calving rate of 78% based on 4,808 calving records. Ninety-one percent of 5,015 calves sired by 260 bulls survived to weaning. Mean heritability estimates and standard deviations for daughter calving rate from posterior distributions were 0.063 ± 0.024, 0.150 ±
0.049, and 0.130 ± 0.047 for linear, threshold, and logistic models, respectively. For calf survival, mean heritability estimates and standard deviations from posterior distributions were 0.049 ± 0.022, 0.160 ± 0.058, and 0.190 ± 0.078 from linear, threshold, and logistic models, respectively. When transformed to an underlying normal scale, linear sire, mixed model, heritability estimates were similar to threshold and logistic sire mixed model estimates. Posterior density distributions of estimated heritabilities from all models were normal. Spearman rank correlations between sire EPD across statistical models were greater than 0.97 for daughter calving rate and for calf survival. Sire EPD had similar ranges across statistical models for daughter calving rate and for calf survival.
Key words: beef cattle, genetic parameter, reproductive trait, statistical method ©2006 American Society of Animal Science. All rights reserved.
INTRODUCTION Calving rate and calf survival have a major impact on herd economic efficiency (Melton, 1995). Both traits have a binomial phenotypic expression but are assumed to have underlying continuous genetic and environmental influences (Wright, 1934; Dempster and Lerner, 1950). Gianola (1982) discussed methodology to estimate genetic parameters for categorical data resulting from an underlying normal distribution. Gianola and Foulley (1983) described a nonlinear method for sire evaluation of categorical data resulting from an underlying normal genetic distribution with a fixed threshold. Heritability is necessary to calculate expected responses to selection and to predict breeding values.
1 Approved for publication by the Director of the Louisiana Agric. Exp. Stn. as Manuscript No. 05-18-0051. 2 Current address: Keygene N.V., Bio-Informatics, P. O. Box 216, 6700 AE Wageningen, the Netherlands. 3 Corresponding author:
[email protected] Received January 5, 2006. Accepted July 17, 2006.
J. Anim. Sci. 2006. 84:3197–3203 doi:10.2527/jas.2006-007
Most estimates of heritability for calving rate and calf survival are relatively low. Deese and Koger (1967) and Buddenberg et al. (1989) reported numerically higher estimates of heritability for calving rate after transforming sire model binomial estimates to the probit scale. Koots et al. (1994) reported average weighted threshold model heritability estimates of 0.17 and 0.10 for calving rate and perinatal mortality, respectively. Riley et al. (2004) reported an estimate of heritability of 0.06 ± 0.05 for preweaning mortality in Brahman calves. Because of the importance of cow fertility and calf survival in beef cattle production systems and the relatively low number of heritability estimates from multibreed populations, the objectives of this study were to estimate the heritability of calving rate and calf survival in a multibreed population with linear, threshold, and logistic, generalized, mixed sire models and to predict sire EPD for daughter calving rate and calf survival rate.
MATERIALS AND METHODS Data were obtained from a long-term rotational crossbreeding study conducted at the Louisiana State Uni-
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versity Agricultural Center Central Station, Baton Rouge. The Committee for Animal Care and Use in the Louisiana State University Agricultural Center approved management aspects for the study. The geographical coordinates for the station are 30°31′N for latitude and 90°08′W for longitude. The land area is 10.6 m above sea level. The average high and low daily temperatures are 23 and 13°C, respectively, the average maximum and minimum daily relative humidity are 88 and 54%, respectively, and the average annual rainfall is 147 cm. The area is classified as subtropical.
Cattle and Management Practices Angus, Brahman, Charolais, and Hereford breeds were involved in a rotational crossbreeding study over 5 generations from 1969 through 1995. Four straightbred and 7 rotation combinations were maintained throughout the study. Rotation mating systems included Angus-Brahman, Charolais-Brahman, Hereford-Brahman, Angus-Brahman-Charolais, Angus-BrahmanHereford, Brahman-Charolais-Hereford, and AngusBrahman-Charolais-Hereford. All rotation combinations were initiated with Brahman first-cross (F1) cows bred to produce backcross calves in 2-breed rotation combinations and 3-breed cross calves in 3- and 4-breed rotation systems. Williams et al. (1990) described the management aspects of the study for the first 4 generations and reported rotation combination means for reproductive traits. In generation 4, about one-half of the straightbred cows were mated to produce Brahman F1 calves. Angus × Brahman, Brahman × Angus, Brahman × Charolais, Charolais × Brahman, Brahman × Hereford, and Hereford × Brahman F1 heifers born in generation 4 were developed for use in generation 5. In generation 5, straightbred cows were mated to produce F1 Brahman cross calves, F1 Brahman cross cows were mated to Gelbvieh or Simmental sires to produce 3-breed cross calves, and rotation cows were mated to produce generation 6 rotation calves or to Gelbvieh and Simmental sires to produce terminal-rotation, cross calves. Each generation lasted 5 years. The first year of each generation involved the exposure of females to sires of the appropriate breed. Calves were born in the second, third, fourth, and fifth year of each generation. Cows in each generation were sold when calves were weaned in the fifth year. All weaned heifer calves that seemed normal were saved, developed for replacements, and accumulated over the 4 calf crops in each generation. During the replacement heifer, accumulation phase in each generation, the heifers born in the first 2 yr were involved in various short-term studies such as calving difficulty (Thrift et al., 1986) and calving at 2 vs. 3 yr of age (DeRouen and Franke, 1989; DeRouen et al., 1994). Heifers born in the third and fourth year of a generation were expected to calve first at 2 yr of age. Calving rate and calf survival data collected on replacement heifers
while being accumulated were not included in this study. Because very few cows in generation 1 had known sire identification, the calving rate data from the first generation were omitted from the analyses for calving rate. Sire of calf in generation 1 was known, and data from this generation were included in the analyses for calf survival. Single-sire breeding herds were composed of 25 to 30 straightbred and crossbred females. Cows were assigned to breeding herds to balance age and breed-type. Sires were purchased from purebred producers in Louisiana as yearlings or 2-yr-olds and selected on the basis of larger size in a contemporary group and from cows with greater calving rates. Few sires were related and none by more than 12.5%. To sample as many bulls as possible, the sires were used for 2 yr and replaced. A large-animal veterinarian, assigned by the LSU School of Veterinary Medicine, was responsible for the herd-health program, which included preventative vaccinations for cows, bulls, and calves and the control of external and internal parasites. Only sires passing a breeding soundness examination were used each year. Breeding seasons began on April 15 each year and were 75 d in length. All calves were weaned during the first week in October each year, at an average age of 220 d. Cows were pregnancy tested in October and were culled only for failing to produce a calf in 2 consecutive years, structural unsoundness due to injuries, or reproductive problems such as abnormal reproductive tracts, rectal or uterine prolapse, etc. No selection pressure was placed on replacement heifers for growth or on cows for calf performance. Cows grazed common Bermuda (Cynodon dactylon) and dallisgrass (Paspalum dilatatum) pastures during the summer. Louisiana S-1 white clover (triflorum repens) was available for grazing during the spring. Cows were wintered on native hay, fortified blackstrap molasses (32% CP), and overseeded ryegrass (Lolium multiflorum). Ad libitum intake of forages and supplemental feedstuffs during the winter was managed to meet the nutritional requirements, based on NRC (2000) recommendations.
Response Traits Calving rate was coded as 1 if a cow calved and 0 if a cow failed to calve. Calf survival was coded as 1 if a calf survived to weaning age and a 0 if a calf failed to survive to weaning age. Stillborn calves and abortions were coded 1 for calving rate and 0 for calf survival. Twin calves were recorded as a single record for calving rate but were deleted from the calf survival analysis.
Statistical Analysis Generalized, mixed sire models were used to estimate heritability of calving rate and calf survival in a multibreed population (Hagger and Hofer, 1989; Mor-
Genetic parameters for reproductive traits
eno et al., 1997). Linear, threshold, and logistic models were considered, and the GLIMMIX macro in the MIXED procedure was used (Littell et al., 1996; SAS Inst. Inc., Cary, NC). The usual mixed model was Y = Xβ + Zs + e, where Y was a vector of ones and zeros representing y observations for calving and calf survival, X was the incidence matrix for the β vector of fixed effects, Z was the incidence matrix for the s vector of random effects of sires within breed of sire, and e was the vector of residual error effects. The fixed effects for calving were sire breed of cow (Angus, Brahman, Charolais, or Hereford), year of record, linear and quadratic effects of cow age in years, and linear covariate effects for breed direct and maternal, additive genetic effects and breed combination direct and maternal, heterosis genetic effects (Eisen et al., 1983; Wyatt and Franke, 1986). For calf survival, the fixed effects were the same as for calving, plus the effects of calf sex and the linear and quadratic effects of birth weight. Sire within breed of sire was included as a random effect in each model. It was expected that the inclusion of direct and maternal breed, additive and heterosis genetic effects accounted for any heterogeneity of variance that existed across breed groups. For the generalized linear mixed models analyses (see Littell et al., 1996), the linear predictors were η = Xβ + Zs, where the conditional distributions for the y|s were binomial, with parameter π for probability of calving or calf survival; and the η = g(π) link functions for the linear, threshold, and logistic models for binomial errors were the identity, probit (inverse normal), and logit link functions, respectively. The generalized linear, mixed sire model was run with responses binomially distributed and with no adjustment to the residual variance. The residual variance of the generalized threshold, mixed sire model was set to 1 (Harville and Mee, 1984; Heringstad et al., 2003), and the residual variance of the generalized logistic, mixed sire model was set to π2/3 (Southey et al., 2003). A convergence criterion of 10−9 for minimizing the residual variance was used for all analyses. Variance components and estimates of heritability were obtained in a Bayesian framework, with Markov chain, Monte Carlo simulation using the nonconjugate analysis of variance (NBVC) methodology described by Wolfinger and Kass (2000). The GLIMMIX macro allowed for specification of the estimation method for variance components (REML), statistical model to fit the data, number of posterior simulations (10,000), priors for random (noninformative) and fixed effects (uniform), minimum residual variance for convergence (10− 9 ), and error assigned to the scale of the link function (linear, threshold, or logistic). Heritability was estimated in each of 10,000 random samples of sire and residual variances for each model and trait. A burn-in was not required with the NBVC methodology. The KDE procedure of SAS was used to approximate the final, hypothesized probability, mass
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density function of heritability, and a posterior smooth function was computed for each statistical model. Sire EPD for daughter calving rate and calf survival were predicted with the linear, threshold, and logistic, generalized, mixed sire models. Breed direct and maternal additive and heterosis genetic effects were omitted from these analyses to avoid adjusting for genetic differences that might be attributable to sires. Omitting breed additive, genetic effects from the models to predict sire EPD within breed resulted in the breed additive effect becoming part of the sire EPD and the sire variance. Maternal additive and heterosis genetic effects were accounted for in the residual variance. All sires were purebred, so no adjustment for heterosis genetic effects in sires was necessary. Sire EPD from the linear mixed model were computed directly by multiplying the sire solutions by 100. Sire EPD from the threshold and logistic mixed sire models were computed by transforming maximum a posteriori (MAP) solutions to a probability scale (Gianola and Foulley, 1983). Sirei EPD for calving rate and calf survival from the threshold model = [Φ(MAPi) − ] × 100, where MAPi = the solution for the ith sire in the underlying scale, φ = the standard normal distribution function, and = the base mean calving rate or calf survival, respectively. Eler et al. (2002, 2004) used similar procedures to predict breeding values for pregnancy rate in heifers. From the logistic model, sirei EPD for calving rate and calf survival were predicted by {exp(MAPi)/[1 + exp(MAPi)] − } × 100, where MAPi and are as defined previously. Spearman rank correlations were computed between the sire EPD from different models.
RESULTS AND DISCUSSION Descriptive statistics for calving rate and calf survival by mating system and breed of sire are given in Table 1. A total of 1,458 cows had 4,808 calving records and a mean 78% calving rate. Calf survival from birth to weaning age for 5,015 calves averaged 91%. Among mating systems, straightbred cows had the lowest calving rate (70%), and first-cross cows in generation 5 had the highest calving rate (84%). Calves born in the rotational mating systems had higher survival rates (92 and 93%), and straightbred calves had lowest survival rate (88%). A total of 30 Angus, 61 Brahman, 33 Charolais, and 32 Hereford sires produced daughters with calving records, and 50 Angus, 61 Brahman, 41 Charolais, 54 Hereford, 16 Gelbvieh, and 37 Simmental sires produced calves with calf survival records. Restricted maximum likelihood estimates of sire and error components of variance for calving rate and calf survival from the generalized mixed sire models run with the NBVC procedure are given in Table 2. Mean estimates and standard deviations of sire and error components of variance from the posterior distributions are given in Table 3. Estimates of sire components of variance in Tables 2 and 3 are similar. Sire components of variance for
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Table 1. Distribution of calving rate (CR) and calf survival (CS) records and mean percent calving rate and calf survival by mating system and breed of sire Mating system
No. of cows
No. of CR records
Mean CR, %
No. of CS records
Mean CS, %
Straightbred Two-breed rotation Three-breed rotation Four-breed rotation First-cross cows Total
494 365 378 122 99 1,458
1,448 1,308 1,409 428 215 4,808
70.0 75.0 82.0 80.0 84.0 78.0
1,560 1,303 1,470 422 240 5,015
88.0 92.0 93.0 93.0 90.0 91.0
No. of sires Breed of sire
CR
CS
No. of daughters
No. of CR records
Mean CR, %
No. of CS records
Mean CS, %
Angus Brahman Charolais Hereford Gelbvieh Simmental Total
30 61 33 32 — — 156
50 61 41 54 16 37 260
313 450 324 280 — — 1,367
1,094 1,613 1,144 957 — — 4,808
78.0 79.0 80.0 76.0 — — 78.0
1,082 1,346 998 1,061 206 322 5,015
94.0 88.0 91.0 92.0 87.0 91.0 91.0
both traits from all 3 statistical models were different from zero (P < 0.05). Shapes of the posterior distributions of heritability from the different models are given in Figures 1 and 2. Distributions of heritability from all models followed a general spherical and symmetrical pattern. The points of density in each of the distributions were calculated with the KDE procedure in SAS. Descriptive statistics of posterior density estimates of heritability are given in Table 4. The generalized linear mixed sire model gave posterior distributions with greater densities for calving rate and calf survival than from the threshold or logistic models. Denser posterior distributions are said to be more informative (more precise; Wolfinger and Kass, 2000; Heringstad et al., 2001, 2003) and suggest a better fit of a model to the data. Mean estimates of heritability ± standard deviation for calving rate from the posterior distributions were 0.063 ± 0.024 for the linear, 0.150 ± 0.049 for the threshold, and 0.130 ± 0.047 for the logistic model. Heritabilities at the mode were similar to mean estimates. The
range, 95% confidence interval, and intraquartile range for estimates of heritability of calving rate from the linear model were less than measures of range for heritability estimates from the threshold and logistic models, which were similar. For calf survival, mean estimates of heritability ± standard deviation from the posterior distributions were 0.049 ± 0.022 for the linear, 0.160 ± 0.058 for the threshold, and 0.190 ± 0.078 for the logistic model. Again, heritabilities at the mode of each distribution were similar to mean estimates of heritability. Ranges of sample estimates of heritability were slightly larger from the threshold and logistic models than from the linear model. Differences in posterior distributions of heritability estimates are clearly illustrated in Figures 1 and 2. Heritability estimates for calving rate and calf survival from the linear mixed sire model were similar to threshold and logistic model estimates when transformed to an underlying normal scale using the formula of Robertson and Lerner (1949). The threshold model
Table 2. Restricted maximum likelihood estimates of sire and error components of variance and heritability for calving rate and calf survival from the 3 models Item Calving rate Sire Error Heritability1 Calf survival Sire Error Heritability1 1
Linear model
Threshold model
Logistic model
0.0023 ± 0.0008* 0.1544 ± 0.0320 0.0587
0.0360 ± 0.0127* 1.00002 0.1389
0.1088 ± 0.0393* 3.28653 0.1281
0.0008 ± 0.0001* 0.0720 ± 0.0072 0.0440
0.0407 ± 0.0178* 1.00002 0.1564
0.1554 ± 0.0393* 3.28653 0.1805
Heritability = 4(sire)/(sire + error). Error variance restricted to 1.00. 3 Error variance restricted to π2/3. *P < 0.05. 2
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Table 3. Mean sire and error components of variance from the independence chain sampling of the posterior distribution (10,000 samples) Item Calving rate Sire Error Calf survival Sire Error
Linear model
Threshold model
Logistic model
0.002 ± 0.001 0.154 ± 0.003
0.038 ± 0.013 1.0001
0.114 ± 0.041 3.2862
0.001 ± 0.000 0.072 ± 0.001
0.042 ± 0.015 1.0001
0.164 ± 0.036 3.2862
1
Error variance restricted to 1.00. Error variance restricted to π2/3.
2
estimates of heritability found in this study were similar to the weighted average threshold model estimates of heritability reported by Koots et al. (1994) for calving rate and perinatal mortality. Meyer et al. (1990) reported heritability estimates of 8, 2, and 9% for calving success of Angus, Hereford and Zebu cross cows, respectively, in Australia, when calving success was scored as 1 and cows not calving were scored as 0. Our linear model estimate of heritability for calf survival is similar to the logistic model estimate of heritability for preweaning mortality in Brahman calves reported by Riley et al. (2004). Koots et al. (1994) reported an average weighted heritability estimate for perinatal mortality of 10% from 9 estimates. Cundiff et al. (1986)
Figure 2. Posterior density estimate of heritability for calf survival for each statistical model. reported heritability estimates for calf survival of 7% within breeds and 11% across breeds. Moreno et al. (1997) demonstrated that positively biased estimates of heritability were observed in a sire model simulation study when there was limited inforTable 4. Descriptive statistics for the posterior distribution of heritability Model
Figure 1. Posterior density estimates of heritability for calving rate for each statistical model.
Linear model Mean (±SD) Range Intra-quartile range 95% confidence interval Density at the mode Heritability at the mode Threshold model Mean (±SD) Range Intra-quartile range 95% confidence interval Density at the mode Heritability at the mode Logistic model Mean (±SD) Range Intra-quartile range 95% confidence interval Density at the mode Heritability at the mode
Calving rate
Calf survival
0.063 ± 0.024 0.190 0.031 0.023 to 0.100 17.10 0.057
0.049 ± 0.022 0.160 0.029 0.012 to 0.096 18.30 0.045
0.150 ± 0.049 0.390 0.064 0.061 to 0.250 8.38 0.140
0.160 ± 0.058 0.470 0.076 0.058 to 0.290 6.98 0.150
0.130 ± 0.047 0.390 0.063 0.054 to 0.240 8.61 0.120
0.190 ± 0.078 0.470 0.095 0.034 to 0.311 5.43 0.180
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mation about the fixed effects. Large numbers of fixed effects with few observations per effect seemed to be the cause of biased estimates. Fixed effects in this study were relatively few, and none had relatively small numbers of observations.
Sire EPD Ranges of sire EPD across statistical models for calving rate were similar. Sire EPD for calving rate ranged from −11.3% for an Angus sire from a logistic generalized mixed sire model to +12.2% for a Charolais sire from a linear mixed sire model. Standard deviations among sire EPD within breed of sire ranged from 3.1 for Hereford sires and a linear mixed sire model to 4.5 for Angus sire EPD from a generalized threshold mixed sire model. Spearman rank correlations among sire EPD for daughter calving rate from different statistical models were 0.99 or higher. Sire EPD for calf survival ranged from a low of −12.8% for an Charolais sire with a generalized mixed sire logistic model to a high of 6.2% for an Angus sire from the linear mixed sire model. Ranges of sire EPD from the linear mixed sire model were generally similar to those from the generalized threshold or logistic mixed sire models. Sire EPD for calf survival ranged further in a negative direction than in a positive direction because the mean calf survival of 91% was near the upper limit of 100%. The mean sire EPD for calf survival was negative for each sire breed except Angus indicating that the distribution was skewed slightly in that direction. Spearman rank correlations among sire EPD for calf survival from different statistical models were greater than 0.97. The sire EPD ranges for daughter calving rate were slightly smaller than the sire EPD range reported by Eler et al. (2002) for daughter first calf pregnancy rate in Nellore heifers. The larger range reported by Eler et al. (2002) could be due to a larger heritability estimate for heifer pregnancy of 0.57 ± 0.01. Evans et al. (1999) suggested that heifer pregnancy data from a large herd over a few generations could be used to predict useful breeding values for future replacement heifers. Generally a sire with a daughter calving rate EPD of 6% should produce daughters with a 12% higher probability of calving than daughters from a sire with a −6% EPD for daughter calving rate. Older sires with more daughters that have multiple records will have higher accuracies for their daughter calving rate EPD than younger sires. Spearman rank correlations between sire EPD across generalized linear sire and nonlinear threshold and logistic sire models indicated the different models gave sire EPD with similar rankings. Weller et al. (1988) found correlations of 0.98 or above between breeding values predicted by linear and threshold models for calf mortality. Phocas and Laloe (2003) suggested that in large data sets such as those from breed associations
where herd sizes range from small to large, a linear sire model might be considered for the prediction of breeding values of categorical traits because of its simplicity and its ability to rank sire breeding values similar to that from threshold models. Other options might involve including a continuous variable such as sire scrotal circumference along with calving rate in a 2trait animal model (Evans et al., 1999; Eler et al., 2004).
IMPLICATIONS Heritability estimates for calving rate and calf survival in a multibreed population were relatively low and similar to those observed in other populations. Generalized linear mixed sire model estimates were similar to generalized threshold and logistic sire mixed models when transformed to an underlying normal distribution. Sire EPD for daughter calving rate and for calf survival ranked similarly across statistical models.
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